The Geometric Reasoner: Manifold-Informed Latent Foresight Search for Long-Context Reasoning
For LLM practitioners needing efficient test-time scaling, TGR offers a training-free method to improve reasoning coverage without high computational cost.
The Geometric Reasoner (TGR) is a training-free framework that improves long-context reasoning by performing manifold-informed latent foresight search with chunk-wise KV cache resets, achieving up to 13 points improvement in AUC on Qwen3-8B with only 1.1–1.3× overhead.
Scaling test-time compute enhances long chain-of-thought (CoT) reasoning, yet existing approaches face a fundamental trade-off between computational cost and coverage quality: either incurring high training expense or yielding redundant trajectories. We introduce The Geometric Reasoner (TGR), a training-free framework that performs manifold-informed latent foresight search under strict memory bounds. At each chunk boundary, TGR scores candidate latent anchors via a lightweight look-ahead estimate combined with soft geometric regularizers that encourage smooth trajectories and diverse exploration. Chunk-wise KV cache resets keep memory linear in chunk length. On challenging math and code benchmarks, TGR improves robust trajectory coverage, measured by the area under the Pass@k curve (AUC), by up to 13 points on Qwen3-8B, with negligible overhead of about 1.1--1.3 times.